How do you refresh Object Mode after quitting Edit Mode
Check if you have added Shape Keys to your model. This might have happened by accident. Shape keys allow you to define vertex location changes relative to the original model, and animate those location changes using a value slider. Kind of like recording a coordinate difference / offset. For character animation, this can be useful (search for corrective shape keys on this site).

When you add a new Key to a model in Blender, its influence parameter is set to 0.0 by default. That means, if you go back out to Object Mode, your model jumps back to its initial state. It's easier to show this in a short video:



As you can see, I'm adding the Basis Key (that's always the unaltered stage of the model) and a Key 1 to the model. I'm going to Edit Mode while Key 1 is still active, so I am defining a change within that key. When I tab back out to Object Mode, my changes disappear. But when I slide that Value Slider all the way to 1.0, my changes are back in place.

If this is your problem, Slide your Key 1 value to one, and then first create a new shape key from mix, and then remove all shape keys, while taking care that the new mixed key is the last one you delete: